RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1977, Volume 22, Issue 2, Pages 231–244 (Mi mz8044)  

This article is cited in 10 scientific papers (total in 10 papers)

Uniform regularization of the problem of calculating the values of an operator

V. V. Arestov

Institute of Mathematics and Mechanics, Ural Scientific Center of the AS of USSR

Abstract: Let $X$ and $Y$ be linear normed spaces, $W$ a set in $X$, $A$ an operator from $W$ into $Y$, and $\mathfrak M$ the set $\mathfrak G$ of all operators or the set $\mathscr L$ of linear operators from $X$ into $Y$. With $\delta\ge0$ we put
$$ \nu(\delta,\mathfrak M)=\inf_{T\in\mathfrak M}\sup_{x\in W}\sup_{\|\eta-x\|_X\le\delta}\|Ax-T\eta\|_Y. $$
We discuss the connection of $\nu(\delta,\mathfrak M)$ with the Stechkin problem on best approximation of the operator $A$ in $W$ by linear bounded operators. Estimates are obtained for $\nu(\delta,\mathfrak M)$ e.g., we write the inequality, where $H(Y)$ is Jung's constant of the space $Y$, and $\Omega(t)$ is the modulus of continuity of $A$ in $W$.

Full text: PDF file (958 kB)

English version:
Mathematical Notes, 1977, 22:2, 618–626

Bibliographic databases:

UDC: 517.5
Received: 24.03.1977

Citation: V. V. Arestov, “Uniform regularization of the problem of calculating the values of an operator”, Mat. Zametki, 22:2 (1977), 231–244; Math. Notes, 22:2 (1977), 618–626

Citation in format AMSBIB
\Bibitem{Are77}
\by V.~V.~Arestov
\paper Uniform regularization of the problem of calculating the values of an operator
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 231--244
\mathnet{http://mi.mathnet.ru/mz8044}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=493442}
\zmath{https://zbmath.org/?q=an:0357.47017}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 618--626
\crossref{https://doi.org/10.1007/BF01780971}


Linking options:
  • http://mi.mathnet.ru/eng/mz8044
  • http://mi.mathnet.ru/eng/mz/v22/i2/p231

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. O. A. Timoshin, “The best approximation to the operator of the second mixed derivative”, Izv. Math., 62:1 (1998), 191–200  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. V. Khromova, “On the moduli of continuity of unbounded operators”, Russian Math. (Iz. VUZ), 50:9 (2006), 67–74  mathnet  mathscinet
    4. Babenko Yu., Skorokhodov D., “Stechkin's Problem for Differential Operators and Functionals of First and Second Orders”, J. Approx. Theory, 167 (2013), 173–200  crossref  isi
    5. V. I. Maksimov, “Calculation of the derivative of an inaccurately defined function by means of feedback laws”, Proc. Steklov Inst. Math., 291 (2015), 219–231  mathnet  crossref  crossref  isi  elib
    6. R. R. Akopian, “Optimal recovery of an analytic function in a doubly connected domain from its approximately given boundary values”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 13–18  mathnet  crossref  mathscinet  elib
    7. R. R. Akopian, “Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error”, Math. Notes, 99:2 (2016), 177–182  mathnet  crossref  crossref  mathscinet  isi  elib
    8. R. R. Akopyan, “Optimal recovery of a function analytic in a disk from approximately given values on a part of the boundary”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 25–37  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Akopyan R.R., “Optimal Recovery of a Derivative of An Analytic Function From Values of the Function Given With An Error on a Part of the Boundary”, Anal. Math., 44:1 (2018), 3–19  crossref  isi
    10. R. R. Akopyan, “Optimalnoe vosstanovlenie analiticheskoi v poluploskosti funktsii po priblizhenno zadannym znacheniyam na chasti granichnoi pryamoi”, Tr. IMM UrO RAN, 24, no. 4, 2018, 19–33  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
    Number of views:
    This page:131
    Full text:50
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019